Technology of forming the competence of plausible reasoning of mathematics students by solving open problems

This research aimed to form a technology for creating reasonable reasoning competence of mathematics students by solving open problems using the help of mathematics and technology, and the research was prepared for this purpose. The research was prepared and designed in the fall academic year of 2022–2023, and 256 students studying in the mathematics department in Kazakhstan participated in the research. An application dimension was prepared for the students participating in the research and they were allowed to participate in this application for 3 weeks. Immediately after the trainings to be given in the research were given, the data collection tool was applied to the participant groups and this information was obtained from them. Keywords: Mathematics, technology, reasoning, distance education;